There are two types of vehicle wheel bearing apparatus, those for a driving wheel and those for a driven wheel. Improvements have been achieved by the reduction of manufacturing cost and the reduction of size and weight to improve fuel consumption. One representative example of such a bearing apparatus of the prior art is shown in FIG. 4.
The vehicle wheel bearing apparatus of FIG. 4 is a so-called third generation type and has a wheel hub 51, an inner ring 52, an outer ring 53, and double row rolling elements 54, 54. The wheel hub 51 has an integrally formed wheel mounting flange 55 to mount a wheel (not shown) at one end. An inner raceway surface 51a is formed on the outer circumferential surface of the wheel hub 51. Also, a cylindrical portion 51b axially extends from the inner raceway surface 51a. Hub bolts 56, to secure the wheel on the flange 55, are equidistantly arranged along the periphery of the flange 55.
The inner ring 52 is press-fit onto the cylindrical portion 51b of the wheel hub 51. The inner ring 52 is formed with an inner raceway surface 52a on its outer circumferential surface. A caulked portion 51c prevents the inner ring 52 from axially slipping off from the cylindrical portion 51b of the wheel hub 51. The caulked portion 51c is formed by radially outwardly deforming the end of the cylindrical portion 51b of the wheel hub 51.
The outer ring 53 has an integrally formed body mounting flange 53b to be mounted on a suspension system (not shown). Double row outer raceway surfaces 53a, 53a are formed on its inner circumferential surface. The double row rolling elements 54 are freely rollably contained between the double row outer raceway surface 53a, 53a and the inner raceway surfaces 51a, 52a, which are arranged opposite to the outer raceway surfaces 53a, 53a. 
The wheel hub 51 is formed by carbon steel which includes carbon of 0.40˜0.80% by weight. The wheel hub 51 is hardened by high frequency induction hardening over a surface region (shown by cross-hatching) from a base of the wheel mounting flange 55 to the cylindrical portion 51b. The caulked portion 51c remains as a non-hardened portion after forging. On the other hand, the inner ring 52 is made of high carbon chrome bearing steel, such as SUJ 2, and is hardened to its core by dip quenching.
Thus, it is possible to realize a vehicle wheel bearing apparatus with a low manufacturing cost, has sufficient durability, and prevents the generation of cracks in the caulked portion 51c. Also, the bearing apparatus prevents the diameter of the inner ring 52, secured by the caulked portion 51c, from being deformed to an extent that causes practical problems. In addition, it is possible to prevent the generation of damages in the inner ring 52, such as cracks during its caulking operation, to keep the pre-load at its proper value. This also reduces the manufacturing cost by reducing the number of parts and the number of manufacturing steps (see Japanese Laid-open Patent Publication No. 129703/1999).
In such a vehicle wheel bearing apparatus of the prior art, a corner “A” (FIG. 5), which is a region that remains in a vacant space when the inner ring 52 is press-fit on the cylindrical portion 51b of the wheel hub 51, is formed by a single radius of curvature, a circular arc. In the vehicle wheel bearing apparatus although it is required to reduce its size to reduce its weight, it is necessary to increase a length “X” (a contacting area) of the abutted region between the end face 52b of the inner ring 52 and the shoulder of the cylindrical portion 51b in order to assure the rigidity of the inner ring 52. However, if the length “X” is increased, the corner “A” will be excessively reduced. Thus, an excessively large stress will be caused in the corner. Accordingly, the mechanical strength of the wheel hub 51 would be extremely reduced especially when a bending moment is repeatedly applied to the bearing apparatus.
An interference problem is caused between the corner “A” and a chamfered portion 52c of the inner ring 52 when the radius of curvature of the single radius is increased in order to reduce the stress caused in the corner “A”. The interference between the corner “A” and the chamfered portion 52c of the inner ring 52 causes misalignment and thus reduces the durability of the inner ring 52. Accordingly, dimensional variation or dispersion should be strictly reduced when machining the corner “A”. However, the strict reduction of the dimensional variation leads to a higher manufacturing cost or expense and thus, its degree is limited. Accordingly, it has been a problem to suppress the stress caused in the corner “A” under heavy duty circumstances.